Ayajña (Ayajna) is one of the names of Śiva-Mahādeva (Siva-Mahadeva). According to the narrative drawn from Mahākāvya and Purāṇa(s), there was a time when Śiva was not entitled to receive the share of Yajña(s). Afterwards, since the destruction of Dakṣayajña (Dakshayajna; the legendary sacrifice performed by Daksha, which Siva destroyed), it became customary to offer a share of yajña to Śiva. However, when he did not receive the yajña-share, he was no less admired and worshiped. Though he started receiving the share of such ritual sacrifice after the incident of Dakṣayajña; it never became essential to perform such rituals to satisfy Him.  The point is, in order to please Aśutośa (Asutosa; one who is pleased with very little offering) Śiva, one does not need to perform strictly-ordered Vedic rituals or yajña(s), He can be pleased by pure and simple devotion, which is beyond such yajña(s) or ritualism. So He is known as Ayajña.